Graviton production in non-inflationary cosmology

We discuss the creation of massless particles in a Universe, which transits from a radiation-dominated era to any other expansion law. We calculate in detail the generation of gravitons during the transition to a matter-dominated era. We show that the resulting gravitons generated in the standard radiation/matter transition are negligible. We use our result to constrain one or more previous matter-dominated era, or any other expansion law, which may have taken place in the early Universe. We also derive a general formula for the modification of a generic initial graviton spectrum by an early matter dominated era.